Just Paul

I think at least 4 hours is best.  Depending on how busy they are it might just take an hour but it is better to be safe and get the most time between flights.  My recollection is that she has to go thru secondary inspection the first time.
 
What POE are you arriving at?

That is our timeline. Not an expedite.  We did do a DCF in Juarez as we were blessed in that I have permanent residency in Mexico and that she obtained her Mexican Residency in about 5 hours (well there was a bit of drama the first time we tried). Our first consulate appointment date was December 27th.  Within two weeks, after checking 3 or 4 times a day, I was able to get a September appointment. Next Monday is her medical and Tuesday for her consulate appointment.
 
Good luck on your journey. 

Sorry for the late reply.  When my wife left the Philippines from Manila she didn't have to pay the travel tax.  They said as long as she had her CFO stamp and  immigrant visa she was exempt.

Just to point out that lawful residency is not the same as citizenship.  You can easily file when he has residency.  If you are waiting for him to be an Italian Citizen you will wait much longer.  There might be an issue where his passport expires during the process.  If so hopefully he can renew it in Italy.
 
I would recommend that  you check with the US embassy  / USCIS in Italy to see if they will allow his asylum residency status to be used as residency for the application or if he has to have "permanent" residency.  Again you might have a timing issue with his passport expiration.  In any case you will be applying via the lockbox in the US.

Research K1/CR1 denials visa more.  In the past, prior to the new policy implementation of Sept 11, 2018,  you can appeal a I-130 decision and not a I-129F.  The CR1 might take longer but it is definitely faster then having to refile the K1. The CR1 is also cheaper and has other benefits. In any case a Tourist Visa is probably not going to happen.
 
We wish you the best in the  process.
~Paul

My Filipina wife and I found it was easier and quicker and actually cheaper to marry in Hong Kong this past March.  We sent in the marriage paperwork 2 weeks before and spent about 5 days in HK for the wedding, filing the report of marriage at the consulate and amending her passport.  Just amending her passport was worth going there.   That part is much longer in the Phils.  The USEM will accept the Hong Kong Marriage certificate.  When we looked at doing in in Phils it was going to take 5 to 8 weeks give or take for the approvals.

My Filipina wife and I found it was easier and quicker and actually cheaper to marry in Hong Kong this past March.  We sent in the marriage paperwork 2 weeks before and spent about 5 days in HK for the wedding, filing the report of marriage at the consulate and amending her passport.  Just amending her passport was worth going there.   That part is much longer in the Phils.  The USEM will accept the Hong Kong Marriage certificate.  When we looked at doing in in Phils it was going to take 5 to 8 weeks give or take for the approvals.

You can use the USPS Express Mail Padded envelope - you might have to order one online - or there is a flat rate medium or large box that paper will lay flat in.    In any case you get tracking and it is  2 or 3 days.    
 
And make sure you have a copy of everything you send.

Here is what i did for to get some Financial proof for my wife:
 
Credit Cards -  Capital One will allow for a spouse without a SSN  - you just use 000 00 0001 if you do it online.  If you call in you might have to hang up and try again to find someone that can do it.   I added her to that account and opened another Capital One with my as primary and her as an authorized user.
Banks -  My Chase Banker would only add if she had an ITIN and provided me with a letter stating so.  BBVA Compass added her without a SSN.   My Credit Union wanted a copy of her ID with and address.   I gave them a copy of her Postal-ID.
ITIN - We obtained a Certified an True copy of her passport at the Consulate in Hong Kong and filed that with the ITIN and the letter from Chase.  Had a number back in about 6 weeks.  I am not sure where to get that certified copy  in the Philippines.  After I got the ITIN I was able to add her to the Chase account and Chase Credit Cards.
 
I did put her on as a beneficiary of my life insurance and added her to the title of an old car.   I also added her name to my cable, power, water and HOA bill.  We also setup a Google Project FI phone in her name.
 
Hope this helps!

Try Google flights to get an idea.   Also consider other flight options.   It was $1400 for my wife to go from Manila to Tijuana a week out.   But it was $150 Manila to Hong Kong and then $ 500 from Hong Kong to Tijuana.

Did she get the CFO stamp yet?

The chat logs are nice but you need the face to face time with lots of photos and proof of trips to see each other.

Just pay the fee, no test to take.  They are at 683 Aurora Blvd, New Manila, Quezon City. Open 8-5pm mon thru friday and 8-12 on saturday.  We were there for about 30 minutes on a wednesday morning.  http://www.aap.org.ph/

My wife got her Filipino Drivers License this past April and then we went to get the International Driving Permit (IDP) at the Philippine Auto Association before we left.  We are currently living in Mexico (I'm also a permanent resident there and I was able to add her to the car insurance for 1 year.  By the time that expires we should have immigrated to the US and if it there is still time on IDP she can drive there for the balance of the year.   
 
If we don't have our interview prior to December we will be going back to the Philippines for Christmas and she can renew her IDP for another year.
 
~P